Introduction

- Finite-time-singularity with noise and damping

The influence of noise on the behavior of nonlinear dynamical system is a recurrent theme in modern statistical physics [1]. In a particular class of systems the nonlinear character gives rise to finite-time-singularities, that is solutions which cease to be valid beyond a particular finite time span. One encounters finite-time-singularities in stellar structure, turbulent flow, and bacterial growth [2, 3, 4]. The phenomenon is also seen in Euler flows and in free-surface-flows [5, 6].

In the context of hydrodynamical flow on a nanoscale [8], where microscopic degrees of freedom come into play, it is a relevant issue how noise influences the hydrodynamical behavior near a finite-time-singularity. Leaving aside the issue of the detailed reduction of the hydrodynamical equations to a nanoscale and the influence of noise on this scale to further study, we assume in the present context that a single variable or ''reaction coordinate'' effectively captures the interplay between the singularity and the noise.